Voigt–Thomson law describes anisotropic magnetoresistance effect in a thin film strip as a relationship between the electric resistivity and the direction of electric current:
ρ ( ϑ ) = ρ 0 + Δ ρ ⋅ c o s 2 ϑ {\displaystyle \rho (\vartheta )=\rho _{0}+\Delta \rho \cdot cos^{2}\vartheta }
where:
ϑ {\displaystyle \vartheta \ } is the angle of direction of current in relation to the direction of magnetic field
ρ 0 {\displaystyle \rho _{0}\ } is the initial resistivity
Δ ρ {\displaystyle \Delta \rho \ } is the change of resistivity (proportional to MR ratio) The equation can also be expressed as:
ρ ( ϑ ) = ρ ∥ ⋅ c o s 2 ϑ + ρ ⊥ ⋅ s i n 2 ϑ {\displaystyle \rho (\vartheta )=\rho _{\parallel }\cdot cos^{2}\vartheta +\rho _{\perp }\cdot sin^{2}\vartheta }
where:
ρ ∥ {\displaystyle \rho _{\parallel }\ } is the parallel component of resistivity
ρ ⊥ {\displaystyle \rho _{\perp }\ } is the perpendicular component
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